Journal ArticleDOI
An equilibrium stress field model for finite element solutions of two-dimensional elastostatic problems
V.B. Watwood,B.J. Hartz +1 more
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In this article, a dual formulation to the usual compatible element model is proposed to provide bounds on the exact solution of a finite element problem, and a suitable equilibrium model for use in a routine manner in the finite element scheme.About:
This article is published in International Journal of Solids and Structures.The article was published on 1968-09-01. It has received 84 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
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Finite element exterior calculus, homological techniques, and applications
TL;DR: Finite element exterior calculus as mentioned in this paper is an approach to the design and understand- ing of finite element discretizations for a wide variety of systems of partial differential equations, which brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretiza- tions which are compatible with the geometric, topological and algebraic structures which underlie well-posedness of the PDE problem being solved.
Journal ArticleDOI
Mixed finite elements for elasticity
Douglas N. Arnold,Ragnar Winther +1 more
TL;DR: The elements presented here are the first ones using polynomial shape functions which are known to be stable, and show stability and optimal order approximation.
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Numerical methods for unilateral problems in solid mechanics
Journal ArticleDOI
Mixed finite element methods for linear elasticity with weakly imposed symmetry
TL;DR: New finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima- tions to both stresses and displacements are constructed.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Book
Energy theorems and structural analysis
TL;DR: In this paper, a generalized theory of the most important energy principles in structural analysis is presented, which derive from two basic complementary theorems denoted as the principles of virtual displacements and virtual forces.